Transverse waves travel at 43.2 m/s in a string that is subjected to a tension of 60.5 N. If the string is 15.9 m long, what is its mass?
A) 0.515 kg
B) 0.597 kg
C) 0.216 kg
D) 0.366 kg

Question

Quizplus · Accepted Answer

The mass of the string can be calculated using the wave speed formula for a string, $v = \sqrt{\frac{T}{\mu}}$, where $v$ is the wave speed, $T$ is the tension in the string, and $\mu$ is the mass per unit length of the string. Rearranging this formula to solve for $\mu$ gives $\mu = \frac{T}{v^2}$. The total mass of the string ($m$) can then be found by multiplying $\mu$ by the length of the string ($L$), so $m = \mu L = \frac{T}{v^2} \times L$. Substituting the given values, $T = 60.5 \, \text{N}$, $v = 43.2 \, \text{m/s}$, and $L = 15.9 \, \text{m}$, we find $m = \frac{60.5}{43.2^2} \times 15.9 \approx 0.515 \, \text{kg}$.

Transverse Waves Travel at 43